Material Forces in Finite Element Discretizations

On material forces and finite element discretizations

The idea of using material forces also termed configurational forces in a computational setting is presented. The theory of material forces is briefly recast in the terms of a non-linear elastic solid. It is shown, how in a computational setting with finite elements (FE) the discrete configurational forces are calculated once the classical field equations are solved. This post-process calculati...

Equivalence Conditions for Finite Volume / Element Discretizations in Cylindrical Coordinates

Abstract. A novel numerical technique for the solution of the compressible flow equations over unstructured grids in a cylindrical reference is presented. The proposed approach is based on a mixed finite volume / finite element method. Equivalence conditions relating the finite volume and the finite element metrics in cylindrical coordinates are derived. Numerical simulations of the explosion a...

A FETI-DP Method for Crouzeix-Raviart Finite Element Discretizations

This paper is concerned with the construction and analysis of a parallel preconditioner for a FETI-DP system of equations arising from the nonconforming Crouzeix-Raviart finite element discretization of a model elliptic problem of second order with discontinuous coefficients. We show that the condition number of the preconditioned problem is independent of the coefficient jumps, and grows only ...

Some Local and Parallel Properties of Finite Element Discretizations

Two-scale Finite Element Discretizations for Partial Differential Equations ∗1)

Some two-scale finite element discretizations are introduced for a class of linear partial differential equations. Both boundary value and eigenvalue problems are studied. Based on the two-scale error resolution techniques, several two-scale finite element algorithms are proposed and analyzed. It is shown that this type of two-scale algorithms not only significantly reduces the number of degree...